scholarly journals Stability Analysis and Optimal Control of a Vector-Borne Disease with Nonlinear Incidence

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Muhammad Ozair ◽  
Abid Ali Lashari ◽  
Il Hyo Jung ◽  
Kazeem Oare Okosun
Keyword(s):  
Optimal Control ◽  
Sensitivity Analysis ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Control Technique ◽  
Global Dynamics ◽  
Nonlinear Incidence ◽  
Vector Borne Disease ◽  
Vector Borne ◽  
The Impact

The paper considers a model for the transmission dynamics of a vector-borne disease with nonlinear incidence rate. It is proved that the global dynamics of the disease are completely determined by the basic reproduction number. In order to assess the effectiveness of disease control measures, the sensitivity analysis of the basic reproductive numberR0and the endemic proportions with respect to epidemiological and demographic parameters are provided. From the results of the sensitivity analysis, the model is modified to assess the impact of three control measures; the preventive control to minimize vector human contacts, the treatment control to the infected human, and the insecticide control to the vector. Analytically the existence of the optimal control is established by the use of an optimal control technique and numerically it is solved by an iterative method. Numerical simulations and optimal analysis of the model show that restricted and proper use of control measures might considerably decrease the number of infected humans in a viable way.

scholarly journals The Hopf Bifurcation Analysis and Optimal Control of a Delayed SIR Epidemic Model

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Abdelhadi Abta ◽  
Hassan Laarabi ◽  
Hamad Talibi Alaoui
Keyword(s):  
Optimal Control ◽  
Hopf Bifurcation ◽  
Critical Value ◽  
Control Measures ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Sir Epidemic Model ◽  
Sir Epidemic ◽  
Saturated Incidence Rate ◽  
The Impact

We propose a delayed SIR model with saturated incidence rate. The delay is incorporated into the model in order to model the latent period. The basic reproductive number R0 is obtained. Furthermore, using time delay as a bifurcation parameter, it is proven that there exists a critical value of delay for the stability of diseases prevalence. When the delay exceeds the critical value, the system loses its stability and a Hopf bifurcation occurs. The model is extended to assess the impact of some control measures, by reformulating the model as an optimal control problem with vaccination and treatment. The existence of the optimal control is also proved. Finally, some numerical simulations are performed to verify the theoretical analysis.

scholarly journals Fractional-Order Modelling and Optimal Control of Cholera Transmission

2021 ◽  
Vol 5 (4) ◽  
pp. 261
Author(s):  
Silvério Rosa ◽  
Delfim F. M. Torres
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Sensitivity Analysis ◽  
Fractional Order ◽  
Control Measures ◽  
Time Interval ◽  
Variable Order ◽  
Effectiveness Analysis ◽  
The Cost ◽  
Derivative Order

A Caputo-type fractional-order mathematical model for “metapopulation cholera transmission” was recently proposed in [Chaos Solitons Fractals 117 (2018), 37–49]. A sensitivity analysis of that model is done here to show the accuracy relevance of parameter estimation. Then, a fractional optimal control (FOC) problem is formulated and numerically solved. A cost-effectiveness analysis is performed to assess the relevance of studied control measures. Moreover, such analysis allows us to assess the cost and effectiveness of the control measures during intervention. We conclude that the FOC system is more effective only in part of the time interval. For this reason, we propose a system where the derivative order varies along the time interval, being fractional or classical when more advantageous. Such variable-order fractional model, that we call a FractInt system, shows to be the most effective in the control of the disease.

Vector Control, Optimal Control, and Vector-Borne Disease Dynamics

2020 ◽  
pp. 267-288
Author(s):  
Michael B. Bonsall
Keyword(s):  
Optimal Control ◽  
Population Genetics ◽  
Population Dynamics ◽  
Vector Control ◽  
Cost Effective ◽  
Disease Suppression ◽  
Medical Interventions ◽  
Vector Borne Disease ◽  
Vector Borne

Understanding methods of vector control is essential to vector-borne disease (VBD) management. Vaccines or standard medical interventions for many VDBs do not exist or are poorly developed so disease control is focused on managing vector numbers and dynamics. This involves understanding not only the population dynamics but also the population genetics of vectors. Using mosquitoes as a case study, in this chapter, the modern genetics-based methods of vector control (self-limiting, self-sustaining) on mosquito population and disease suppression will be reviewed. These genetics-based methods highlight the importance of understanding the interplay between genetics and ecology to develop optimal, cost-effective solutions for control. The chapter focuses on how these genetics-based methods can be integrated with other interventions, and concludes with a summary of regulatory and policy perspectives about the use of these approaches in the management of VBDs.

scholarly journals Stability and Hopf Bifurcation of a Vector-Borne Disease Model with Saturated Infection Rate and Reinfection

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Zhixing Hu ◽  
Shanshan Yin ◽  
Hui Wang
Keyword(s):  
Hopf Bifurcation ◽  
Infection Rate ◽  
Disease Model ◽  
Endemic Equilibrium ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Cure Rate ◽  
Vector Borne Disease ◽  
Vector Borne ◽  
The Stability

This paper established a delayed vector-borne disease model with saturated infection rate and cure rate. First of all, according to the basic reproductive number R0, we determined the disease-free equilibrium E0 and the endemic equilibrium E1. Through the analysis of the characteristic equation, we consider the stability of two equilibriums. Furthermore, the effect on the stability of the endemic equilibrium E1 by delay was studied, the existence of Hopf bifurcations of this system in E1 was analyzed, and the length of delay to preserve stability was estimated. The direction and stability of the Hopf bifurcation were also been determined. Finally, we performed some numerical simulation to illustrate our main results.

OPTIMAL CONTROL OF VECTOR-BORNE DISEASE WITH DIRECT TRANSMISSION

2015 ◽  
Vol 76 (13) ◽  
Author(s):  
Nurul Aida Nordin ◽  
Rohanin Ahmad ◽  
Rashidah Ahmad
Keyword(s):  
Dynamical System ◽  
Optimal Control ◽  
Optimal Control Theory ◽  
Existence And Uniqueness ◽  
Blood Donation ◽  
Direct Transmission ◽  
Vector Borne Disease ◽  
Indirect Transmission ◽  
Vector Borne ◽  
Vector Control Strategy

This paper introduces the usage of three controls as a way to reduce the occurrence of vector-borne disease. The governing equation of the dynamical system used in this paper describes both direct and indirect transmission mode of vector-borne disease. This means that the disease can be transmitted in two different ways. First, it can be transmitted through mosquito bites and the other is through human blood transfusion. The three controls that are incorporated in the dynamical system include a measurement of basic practice for blood donation procedure, self-prevention effort and vector control strategy by health authority. The optimality system of the three controls is characterized using optimal control theory and the existence and uniqueness of the optimal control are established. Then, the effect of the incorporation of the three controls is investigated by performing numerical simulation. 

scholarly journals PO 8505 LEISHMANIASIS IN ANGOLA – AN EMERGING DISEASE?

2019 ◽  
Vol 4 (Suppl 3) ◽  
pp. A47.3-A48
Author(s):  
Sofia Cortes ◽  
André Pereira ◽  
Jocelyne Vasconcelos ◽  
Joana P Paixão ◽  
Joltim Quivinja ◽  
...  
Keyword(s):  
Cutaneous Leishmaniasis ◽  
Neglected Tropical Diseases ◽  
Epidemiological Studies ◽  
Sequencing Analysis ◽  
Vector Borne Disease ◽  
Health Authorities ◽  
African Patient ◽  
Control Programmes ◽  
Vector Borne ◽  
The Impact

BackgroundPoverty, lack of resources, inadequate treatments and control programmes exacerbate the impact of infectious diseases in the developing world. Leishmaniasis is a vector-borne disease that is among the ten major neglected tropical diseases. Although endemic in more than 90 countries, the ones most affected, representing over 90% of new cases, are Bangladesh, Brazil, Ethiopia, India, Kenya, Nepal, and Sudan. In Africa south of the equator, the impact of leishmaniasis is much lower. In several countries, like Angola, little is known about this infectious neglected disease. In the 1970s, a group of Portuguese researchers described three cases of cutaneous leishmaniasis in children from Huambo district and in the 1990s visceral leishmaniasis was diagnosed in an African patient. More recently a canine survey in Luanda revealed two Leishmania-infected dogs.After some suspected cases of human cutaneous leishmaniasis in Huambo region in 2017, the Angola health authorities and the Instituto de Higiene e Medicina Tropical (IHMT), Lisbon, Portugal, established a collaboration to analyse samples from some suspected cases.MethodsThree paraffin-embedded human skin samples from dermatological lesions were sent to IHMT for molecular analysis. After DNA extraction, PCR was performed by using four protocols with different molecular markers.ResultsOne PCR protocol using a nested approach was positive in two of the samples. Sequencing analysis confirmed Leishmania sp. DNA.ConclusionThis was the first time that suspected human cutaneous samples were screened for leishmaniasis by molecular methods with detection of Leishmania sp. DNA. These preliminary studies highlight the need for higher awareness of health professionals for leishmaniasis clinical forms, to recognise risk factors and the epidemiological features of leishmaniasis in the Huambo province. It would be relevant to perform further epidemiological studies to confirm if this vector-borne disease could be emergent in this country.

scholarly journals Modeling the Effects of Helminth Infection on the Transmission Dynamics of Mycobacterium tuberculosis under Optimal Control Strategies

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Aristide G. Lambura ◽  
Gasper G. Mwanga ◽  
Livingstone Luboobi ◽  
Dmitry Kuznetsov
Keyword(s):  
Optimal Control ◽  
Equilibrium Point ◽  
Drug Administration ◽  
Mass Drug Administration ◽  
Helminth Infection ◽  
Reproduction Number ◽  
Control Strategies ◽  
Active Tuberculosis ◽  
Control Measures ◽  
The Impact

A deterministic mathematical model for the transmission and control of cointeraction of helminths and tuberculosis is presented, to examine the impact of helminth on tuberculosis and the effect of control strategies. The equilibrium point is established, and the effective reproduction number is computed. The disease-free equilibrium point is confirmed to be asymptotically stable whenever the effective reproduction number is less than the unit. The analysis of the effective reproduction number indicates that an increase in the helminth cases increases the tuberculosis cases, suggesting that the control of helminth infection has a positive impact on controlling the dynamics of tuberculosis. The possibility of bifurcation is investigated using the Center Manifold Theorem. Sensitivity analysis is performed to determine the effect of every parameter on the spread of the two diseases. The model is extended to incorporate control measures, and Pontryagin’s Maximum Principle is applied to derive the necessary conditions for optimal control. The optimal control problem is solved numerically by the iterative scheme by considering vaccination of infants for Mtb, treatment of individuals with active tuberculosis, mass drug administration with regular antihelminthic drugs, and sanitation control strategies. The results show that a combination of educational campaign, treatment of individuals with active tuberculosis, mass drug administration, and sanitation is the most effective strategy to control helminth-Mtb coinfection. Thus, to effectively control the helminth-Mtb coinfection, we suggest to public health stakeholders to apply intervention strategies that are aimed at controlling helminth infection and the combination of vaccination of infants and treatment of individuals with active tuberculosis.

scholarly journals On the Global Dynamics of a Vector-Borne Disease Model with Age of Vaccination

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Stanislas Ouaro ◽  
Ali Traoré
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Mass Action ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Vector Borne Disease ◽  
Special Cases ◽  
Vector Borne ◽  
The Basic Reproduction Number

We study a vector-borne disease with age of vaccination. A nonlinear incidence rate including mass action and saturating incidence as special cases is considered. The global dynamics of the equilibria are investigated and we show that if the basic reproduction number is less than 1, then the disease-free equilibrium is globally asymptotically stable; that is, the disease dies out, while if the basic reproduction number is larger than 1, then the endemic equilibrium is globally asymptotically stable, which means that the disease persists in the population. Using the basic reproduction number, we derive a vaccination coverage rate that is required for disease control and elimination.

scholarly journals Modeling the Impact of Optimal Control Strategies on the Dynamics of Zika Virus Disease Using the Sterile Insect Technology

2020 ◽  
pp. 13-33
Author(s):  
Atokolo William ◽  
Akpa Johnson ◽  
Daniel Musa Alih ◽  
Olayemi Kehinde Samuel ◽  
C. E. Mbah Godwin
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Zika Virus ◽  
Human Population ◽  
Necessary Conditions ◽  
Virus Disease ◽  
Control Strategies ◽  
Control Measures ◽  
Optimal Control Strategy ◽  
The Impact

This work is aimed at formulating a mathematical model for the control of zika virus infection using Sterile Insect Technology (SIT). The model is extended to incorporate optimal control strategy by introducing three control measures. The optimal control is aimed at minimizing the number of Exposed human, Infected human and the total number of Mosquitoes in a population and as such reducing contacts between mosquitoes and human, human to human and above all, eliminates the population of Mosquitoes. The Pontryagin’s maximum principle was used to obtain the necessary conditions, find the optimality system of our model and to obtain solution to the control problem. Numerical simulations result shows that; reduction in the number of Exposed human population, Infected human population and reduction in the entire population of Mosquito population is best achieved using the optimal control strategy.

scholarly journals Survey of protozoan vector-borne diseases in dogs from Atlantic Rainforest fragment around Billings Dam, São Paulo, Brazil

2020 ◽  
Vol 50 (9) ◽  
Author(s):  
Roberta Carvalho de Freitas e Azevedo ◽  
Giovanna Stefani Nosberto Castelli ◽  
Ryan Emiliano da Silva ◽  
Jaciara de Oliveira Jorge Costa ◽  
Renata Tonhosolo ◽  
...  
Keyword(s):  
Animal Health ◽  
Companion Animals ◽  
Sao Paulo ◽  
Control Measures ◽  
Molecular Diagnostic ◽  
São Paulo ◽  
Vector Borne Diseases ◽  
Babesia Vogeli ◽  
Vector Borne ◽  
The Impact

ABSTRACT: Vector-borne diseases are currently one of the biggest public health concerns worldwide. Dogs, being the closest companion animals to humans, are considered the main reservoir of some of these diseases in the urban environment. Therefore, the study of the disease behavior in dogs can help to understand the disease affecting human health. Serological and molecular diagnoses of Babesia vogeli, Rangelia vitalli, Leishmania infantum, and other trypanosomatids, were performed by immunochromatographic and PCR assays, respectively, on dogs in a dog shelter located in an Atlantic Forest fragment near the Billings Dam, São Bernardo do Campo, São Paulo-Brazil. Our molecular diagnostic results showed a high prevalence of Babesia vogeli, at 20.9% (17/81). No other protozoan was detected in any of the tests. Determining the prevalence of major vector-borne diseases is essential to establish preventive and control measures for zoonotic diseases in animals kept in shelters, in order to minimize the impact of vector-borne diseases on animal health.

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